Final answer:
The term "indefatigable" in the Lady Roosevelt passage best defines as 'tireless', which refers to someone's enduring stamina and persistent efforts.
Step-by-step explanation:
Based on the content of the passage featuring Lady Roosevelt, the best definition for the word "indefatigable" is tireless. The term is often used to describe a person who possesses an impressive stamina or persistence, someone who never seems to get tired, both physically and metaphorically, in the pursuit of their endeavors. This meaning fits better with the context than 'enthusiastic', 'ambitious', or 'sympathetic', as it speaks directly to an enduring quality of effort, rather than just passion, drive, or compassion.